PSG are seeking to buy into David Beckham's MLS Miami FC franchise.
BBC Sport says sources close to the proposed deal say Qatar Sports Investment are just one of many interested groups.
Manchester United legend Beckham ended his playing career with PSG in 2012-13.
He will remain heavily involved in the project in the event of any sale.
Beckham has strong links to Qatar and recently defended its right to host the 2022 World Cup, along with Russia in 2018.
He said in December: "Whether it's corrupt or not, those countries have been chosen.
"People need to get behind that. It's all about bringing football to new countries. I think they should stick with it."